From 53a0fcbdea66eeaa09f64091f4f33daa230bea3f Mon Sep 17 00:00:00 2001 From: Lusina <12752833+BrianLusina@users.noreply.github.com> Date: Fri, 9 Jan 2026 13:44:42 +0300 Subject: [PATCH 1/2] feat(bit-manipulation, count-bits): count number of bits --- bit_manipulation/number_of_1_bits/README.md | 71 ++++++++++++++++++ bit_manipulation/number_of_1_bits/__init__.py | 11 +++ .../number_of_one_bits_solution_1.png | Bin 0 -> 46500 bytes .../number_of_one_bits_solution_10.png | Bin 0 -> 51611 bytes .../number_of_one_bits_solution_11.png | Bin 0 -> 44915 bytes .../number_of_one_bits_solution_12.png | Bin 0 -> 67668 bytes .../number_of_one_bits_solution_13.png | Bin 0 -> 52164 bytes .../number_of_one_bits_solution_14.png | Bin 0 -> 45758 bytes .../number_of_one_bits_solution_15.png | Bin 0 -> 62141 bytes .../number_of_one_bits_solution_2.png | Bin 0 -> 42691 bytes .../number_of_one_bits_solution_3.png | Bin 0 -> 65709 bytes .../number_of_one_bits_solution_4.png | Bin 0 -> 50468 bytes .../number_of_one_bits_solution_5.png | Bin 0 -> 57956 bytes .../number_of_one_bits_solution_6.png | Bin 0 -> 63888 bytes .../number_of_one_bits_solution_7.png | Bin 0 -> 50289 bytes .../number_of_one_bits_solution_8.png | Bin 0 -> 41752 bytes .../number_of_one_bits_solution_9.png | Bin 0 -> 68033 bytes .../test_number_of_one_bits.py | 23 ++++++ 18 files changed, 105 insertions(+) create mode 100644 bit_manipulation/number_of_1_bits/README.md create mode 100644 bit_manipulation/number_of_1_bits/__init__.py create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_1.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_10.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_11.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_12.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_13.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_14.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_15.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_2.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_3.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_4.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_5.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_6.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_7.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_8.png create mode 100644 bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_9.png create mode 100644 bit_manipulation/number_of_1_bits/test_number_of_one_bits.py diff --git a/bit_manipulation/number_of_1_bits/README.md b/bit_manipulation/number_of_1_bits/README.md new file mode 100644 index 00000000..12ea2e20 --- /dev/null +++ b/bit_manipulation/number_of_1_bits/README.md @@ -0,0 +1,71 @@ +# Number of 1 Bits + +Write a function that takes a 32-bit binary representation of an unsigned integer n and returns the count of its 1 bits. + +The binary representation of an unsigned integer is a sequence of 0s and 1s that represents the integer's value using +base-2 notation. An example of the 32-bit binary representation of an unsigned integer 13 is 00000000000000000000000000001101. + +## Constraint + +- The input must be a 32-bit binary representation of an unsigned integer. + +> Note: The input is passed to the function as an unsigned integer variable. In this lesson, we have displayed it as a +> string of binary numbers solely for visualization purposes. + + +## Solution + +The first attempt to solve this would be to iterate over each bit in the 32-bit representation and keep increasing the +count, representing the number of 1 bits, every time we encounter the digit 1. This is the correct way to solve this +problem, and it even takes constant time and space complexity. However, this approach requires us to perform 32 +iterations regardless of the number of 1 bits, which makes it a less efficient approach, specifically for integers with +a small number of 1 bits. For example, there are only three 1 bits in the unsigned integer 13, but we'll have to iterate +the entire 32 times to get to this number. +To avoid any unnecessary iterations, we can use bitwise manipulation to efficiently count the number of 1 bits in the +given unsigned integer. Here, we'll iterate through the bits of the binary representation that are actually 1s. This +means it only performs iterations equal to the number of 1 bits in the binary representation of the integer. For example, +if the given integer is 12 with the binary representation of 00000000000000000000000000001100, the loop will iterate only +twice, which is highly efficient. + +First, we'll initialize a counter, count, to keep track of the number of 1 bits in the 32-bit binary representation of +an unsigned integer. Then, we'll start a loop that continues as long as the integer n is not zero, i.e., there is no 1 bit +left in the integer. This loop will iterate through each bit of the binary representation of n, starting from the least +significant bit. In each iteration: + +> The least significant bit is the rightmost bit in the binary representation of a number. + +- Check whether the least significant bit of n is equal to 1 using the bitwise AND operation. + - If the last bit is 1, increment the count by 1. + - Otherwise, continue with the loop. +- Once we are done checking the current bit, right-shift n by one position using the right bitwise shift operator. This + operation effectively shifts all bits one place to the right, discarding the last bit and making the next bit the new + least significant bit. + +Eventually, count will have the total number of 1 bits, so we'll return it as the final result. + +Let’s look at the following illustration to get a better understanding of the solution: + +![Solution 1](./images/solutions/number_of_one_bits_solution_1.png) +![Solution 2](./images/solutions/number_of_one_bits_solution_2.png) +![Solution 3](./images/solutions/number_of_one_bits_solution_3.png) +![Solution 4](./images/solutions/number_of_one_bits_solution_4.png) +![Solution 5](./images/solutions/number_of_one_bits_solution_5.png) +![Solution 6](./images/solutions/number_of_one_bits_solution_6.png) +![Solution 7](./images/solutions/number_of_one_bits_solution_7.png) +![Solution 8](./images/solutions/number_of_one_bits_solution_8.png) +![Solution 9](./images/solutions/number_of_one_bits_solution_9.png) +![Solution 10](./images/solutions/number_of_one_bits_solution_10.png) +![Solution 11](./images/solutions/number_of_one_bits_solution_11.png) +![Solution 12](./images/solutions/number_of_one_bits_solution_12.png) +![Solution 13](./images/solutions/number_of_one_bits_solution_13.png) +![Solution 14](./images/solutions/number_of_one_bits_solution_14.png) +![Solution 15](./images/solutions/number_of_one_bits_solution_15.png) + +### Time Complexity + +In the worst case, the number of iterations in the loop can go up to 32, which is a fixed number. Therefore, the overall +time complexity for this solution is O(1). + +### Space Complexity + +The space complexity of this solution is O(1). \ No newline at end of file diff --git a/bit_manipulation/number_of_1_bits/__init__.py b/bit_manipulation/number_of_1_bits/__init__.py new file mode 100644 index 00000000..9135d0b1 --- /dev/null +++ b/bit_manipulation/number_of_1_bits/__init__.py @@ -0,0 +1,11 @@ +def count_bits(n: int) -> int: + count = 0 + + while n: + # Check the least significant bit by using AND + if n & 1: + count += 1 + # Right-shift the number to move to the next bit + n >>= 1 + + return count diff --git a/bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_1.png b/bit_manipulation/number_of_1_bits/images/solutions/number_of_one_bits_solution_1.png new file mode 100644 index 0000000000000000000000000000000000000000..724e79e15b84929f5010b7484986354ceecf237a GIT binary patch literal 46500 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